Background map with Basemap

Basemap is probably the best option to draw a connection map with python. It provides a function calleddrawgreatcircle() that draws the connection using great circles. Great circles are arcs that gives a better appearance than straight lines.

Most basic connection map with Python and Basemap.

Show connection between a few cities with great circles.

This is the result when you visualize the connection between 7 major world cities:

A connection map between 7 cities made with Python and Basemap